Complexity analysis of source activity underlying the neuromagnetic somatosensory steady-state response
Introduction
Characterizing functionally specific brain regions and describing their functional integration are two complimentary, not mutually exclusive, issues studied in neuroscience. One possible paradigm to tackle these issues is to consider the brain as a complex system (Jirsa and McIntosh, 2007). This approach focuses on complexity, a broadly defined property characterizing a highly variable system with many parts whose behaviors strongly depend on the behavior of other parts (Deisboeck and Kresh, 2006). Information-theoretic tools provide many ways to estimate complexity of brain signals. In general, a complex system can be characterized by its entropy, which can be related to uncertainty contained in signals. Typically, higher entropy is associated with disorder, uncertainty and unpredictability, whereas lower entropy is related to a high degree of organization. Traditional methods for estimating entropy can lose much information related to temporal properties of the signal. Based on nonlinear dynamics, a number of techniques for signal analysis have been recently designed to yield more details on inherent dynamic properties of brain activity (Stam, 2005).
Pincus (1991) developed a measure of signal regularity closely related to the Kolmogorov entropy (Grassberger and Procaccia, 1983), interpreted as an averaged rate of information produced by a dynamic system. Called approximate entropy, this statistic can be applied for short and noisy time series. Approximate entropy searches for epochs that are similar in one multidimensional representation of the original signal, and will remain similar in a space with increased dimensionality. In an attempt to reduce the bias in estimating the approximate entropy due to calculating self-matches in the signal patterns, Richman and Moorman (2000) proposed the sample entropy statistic. Similar to sample entropy in design and concept, cross-sample entropy as a refined version of cross approximate entropy was introduced as a measure of synchrony between bivariate time series (Richman and Moorman, 2000). Cross-sample entropy was designed to compare epochs from one signal with those of the second, identifying the averaged degree of similarity between them.
Recent complexity-based studies have proven useful in characterizing pathological states of brain activity such as in epilepsy and psychiatric disorders or brain dementia. Applying approximate entropy analysis to the different epochs of epileptic seizure time series, Radhakrishnan and Gangadhar (1998) observed increased complexity values at the beginning and the end of the seizure. Approximate entropy was also used to characterize the depth of anaesthetic effect using electroencephalography (EEG) recordings (Bruhn et al., 2000). A number of studies applied complexity-based tools to examine brain activity in patients with Alzheimer's disease (AD) (Hornero et al. (2009) for a review). In particular, Absolo et al. (2005) found decreased irregularity of EEG rhythms in AD patients, compared to control subjects. Similar to EEG, magnetoencephalography (MEG) activity was reported to be less complex and more regular in AD patients than in control subjects (Gmez et al., 2009). In addition, in normal brain, a comparative analysis of EEG data in five age groups, using multi-scale entropy based on sample entropy (Costa et al., 2002), indicated that brain variability increases with maturation, reflecting a broader repertoire of metastable brain states and more rapid transitions among them (McIntosh et al., 2008).
The common feature of the aforementioned studies is that they differentiate brain activity in different states based on EEG/MEG scalp measurements that do not directly represent localized brain regions in the vicinity of one electrode. Due to volume conduction, the measured potentials reflect a summed signal from simultaneously active, underlying current sources when signals of the sources become filtered and spread out across all the electrodes (Nunez and Shrinivasan, 2005). The translation to source space would be a logical extension, particularly with the recent refinements in source-space projections through the beam-former solutions. This study shows that sample entropy and cross-sample entropy statistics can be sensitive enough to work at the level of individual regions and discriminate the dynamics of neuromagnetic activity between different sources.
This study illustrates the possibility to characterize brain activity and interactions between sources using the concept of complexity with application to the somatosensory steady-state response (SSSR) evoked by a periodic tactile signal. Oscillatory steady-state response is a phenomenon observed as a reaction to applying trains of periodically repeated stimuli, in contrast to temporal patterns of transient signal changes caused by the onsets of stimulus trains (Nangini et al., 2006). Typically the SSSR, which is observed at the frequency of the driving stimulus, is smaller than the transient response, reaching its maximal amplitudes between 21 and 26 Hz (Snyder, 1992). It was suggested that the pattern of synchronization between neuronal groups dynamically determines the pattern of neuronal interactions (Womelsdorf et al., 2007). Following the idea of functional connectivity modulated by synchronous oscillations, Bardouille and Ross (2008) applied a statistic measure called intertrial coherence (ITC) (Stapells et al., 1987). In an attempt to find brain areas with the SSSR with consistent phase relations to the stimulus, they measured the degree of phase-locking inherent in a given signal. Various sensorimotor areas were identified in individual source ITC maps, but only the primary somatosensory area (SI) contralateral to stimuli was consistently identified across subjects.
ITC is calculated in the space spanned by the real component of the signal and the imaginary part reconstructed from the original signal. In essence, ITC is based on a two-dimensional reconstruction of the dynamical system underlying the observed signal. Nonlinear techniques based on multidimensional reconstruction of the dynamics of brain activity through time delay embedding might be viewed as the platform to provide a generalization of the two-dimensional complex space. The goal would be to find brain areas that are co-activated with the SSSR having consistent regular patterns. Characterizing the involved brain regions and their interaction within a wide range network would contribute to understanding the principles underlying somatosensory perception. In this study, we identified the loci of somatosensory activation, using sample entropy as a measure of complexity (regularity), and subsequently explored synchrony in the activation network, performing the cross-sample entropy analysis.
Section snippets
Experiment
MEG data were collected at a sample rate of 1250 Hz with a bandwidth of 0–300 Hz using a 151-channel whole-head first-order gradiometer system (VSM Medtech, Port Coquitlam, BC, Canada). Subjects were seated upright with their head resting in the helmed shaped scanner. Head localization coils were placed on the nasion, and left and right pre-auricular points for co-registration of MEG data with anatomical MR images. A small elastic air bladder was fitted to the right index finger pad.
Simulations
This section describes “proof-of-principle” simulations emphasizing the method based on complexity analysis described above. The objective is to demonstrate the performance of the sample and cross-sample entropy statistics in the presence of two active dipoles coded as SI and SII. We chose one anatomical MRI data set from the pool of subjects. Specified in Talaraich coordinate system, two source locations were x = −40 m [L], y = −20 mm [P], and z = 84 mm [S] for SI, and x = −50 m [L], y = 0 mm [P], and z =
Discussion
Somatosensory cortical activity is encoded topographically according to the body surface. The discovery of this somatotopic organization of the somatosensory cortex SI in humans can be traced back to Penfield and Boldrey (1937). In addition to SI, other brain areas were found to be sensitive to tactile stimuli, including the PPC regions, the secondary somatosensory cortex (SII), supplementary motor area (SMA), and primary motor cortex (MI) (Forss et al., 2001, Hyvarinen, 1982, Nangini et al.,
Acknowledgments
We wish to thank Maria Tassopoulos for her assistance in preparing this manuscript.
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